Calculus

Schedule:

Section

Days/Times

Location

Instructor

Class

001 LEC

MoWeFr 12:00PM - 12:59PM

Valley Life Sciences 2050

Alexander Paulin

18173

Units

Enrollment Status

4

Open

Additional Information:

Prerequisites: Three and one-half years of high school math, including trigonometry and analytic geometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic test, or 32. Consult the mathematics department for details. Students with AP credit should consider choosing a course more advanced than 1A

Description: This sequence is intended for majors in engineering and the physical sciences. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.

Calculus

Schedule:

Section

Days/Times

Location

Instructor

Class

002 LEC

MoWeFr 9:00AM - 9:59AM

Dwinelle 155

Alexander Paulin

18174

Units

Enrollment Status

4

Open

Additional Information:

Prerequisites: Three and one-half years of high school math, including trigonometry and analytic geometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic test, or 32. Consult the mathematics department for details. Students with AP credit should consider choosing a course more advanced than 1A

Description: This sequence is intended for majors in engineering and the physical sciences. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.

Calculus

Schedule:

Section

Days/Times

Location

Instructor

Class

003 LEC

TuTh 3:30PM - 4:59PM

Boalt 175

Sug Woo Shin

18175

Units

Enrollment Status

4

Open

Additional Information:

Prerequisites: Three and one-half years of high school math, including trigonometry and analytic geometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic test, or 32. Consult the mathematics department for details. Students with AP credit should consider choosing a course more advanced than 1A

Description: This sequence is intended for majors in engineering and the physical sciences. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.

Methods of Mathematics: Calculus, Statistics, and Combinatorics

Schedule:

Additional Information:

Prerequisites: Three and one-half years of high school math, including trigonometry and analytic geometry

Description: This sequence is intended for majors in the life sciences. Introduction to differential and integral calculus of functions of one variable. Representation of data, elementary probability theory, statistical models, and testing.

Methods of Mathematics: Calculus, Statistics, and Combinatorics

Schedule:

Additional Information:

Prerequisites: Three and one-half years of high school math, including trigonometry and analytic geometry

Description: This sequence is intended for majors in the life sciences. Introduction to differential and integral calculus of functions of one variable. Representation of data, elementary probability theory, statistical models, and testing.

Analytic Geometry and Calculus

Schedule:

Section

Days/Times

Location

Instructor

Class

001 LEC

MoWeFr 8:00AM - 8:59AM

Dwinelle 155

Mihaela Ifrim

18231

Units

Enrollment Status

3

Open

Additional Information:

Prerequisites: Three years of high school math, including trigonometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic exam, or 32. Consult the mathematics department for details

Description: This sequence is intended for majors in the life and social sciences. Calculus of one variable; derivatives, definite integrals and applications, maxima and minima, and applications of the exponential and logarithmic functions.

Analytic Geometry and Calculus

Schedule:

Section

Days/Times

Location

Instructor

Class

002 LEC

MoWeFr 10:00AM - 10:59AM

Dwinelle 155

Emiliano Gomez

18232

Units

Enrollment Status

3

Open

Additional Information:

Prerequisites: Three years of high school math, including trigonometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic exam, or 32. Consult the mathematics department for details

Description: This sequence is intended for majors in the life and social sciences. Calculus of one variable; derivatives, definite integrals and applications, maxima and minima, and applications of the exponential and logarithmic functions.

Analytic Geometry and Calculus

Schedule:

Section

Days/Times

Location

Instructor

Class

001 LEC

MoWeFr 3:00PM - 3:59PM

Valley Life Sciences 2050

Antonio Montalban

18309

Units

Enrollment Status

3

Closed

Additional Information:

Prerequisites: 16A

Description: Continuation of 16A. Application of integration of economics and life sciences. Differential equations. Functions of many variables. Partial derivatives, constrained and unconstrained optimization.

Freshman Seminars

Schedule:

Section

Days/Times

Location

Instructor

Class

001 SEM

We 11:00AM - 11:59AM

Evans 939

Francisco Grunbaum

18085

Units

Enrollment Status

1

Open

Additional Information:

Prerequisites:

Description: The Berkeley Seminar Program has been designed to provide new students with the opportunity to explore an intellectual topic with a faculty member in a small-seminar setting. Berkeley Seminars are offered in all campus departments, and topics vary from department to department and semester to semester.

Office:

Office Hours:

Required Text:

Recommended Reading:

Grading: The grading option will be decided by the instructor when the class is offered. Final exam required.

Freshman Seminars

Schedule:

Section

Days/Times

Location

Instructor

Class

002 SEM

We 10:00AM - 11:59AM

Evans 891

Nicolai Reshetikhin

34446

Units

Enrollment Status

1

Open

Additional Information:

Prerequisites:

Description: The Berkeley Seminar Program has been designed to provide new students with the opportunity to explore an intellectual topic with a faculty member in a small-seminar setting. Berkeley Seminars are offered in all campus departments, and topics vary from department to department and semester to semester.

Office:

Office Hours:

Required Text:

Recommended Reading:

Grading: The grading option will be decided by the instructor when the class is offered. Final exam required.

Berkeley Connect

Schedule:

Section

Days/Times

Location

Instructor

Class

001 DIS

We 6:00PM - 6:59PM

Evans 41

18954

Units

Enrollment Status

1

Closed

Additional Information:

Prerequisites:

Description: Berkeley Connect is a mentoring program, offered through various academic departments, that helps students build intellectual community. Over the course of a semester, enrolled students participate in regular small-group discussions facilitated by a graduate student mentor (following a faculty-directed curriculum), meet with their graduate student mentor for one-on-one academic advising, attend lectures and panel discussions featuring department faculty and alumni, and go on field trips to campus resources. Students are not required to be declared majors in order to participate.

Berkeley Connect

Schedule:

Section

Days/Times

Location

Instructor

Class

002 DIS

Tu 6:00PM - 6:59PM

Evans 41

Ben Wormleighton

18955

Units

Enrollment Status

1

Open

Additional Information:

Prerequisites:

Description: Berkeley Connect is a mentoring program, offered through various academic departments, that helps students build intellectual community. Over the course of a semester, enrolled students participate in regular small-group discussions facilitated by a graduate student mentor (following a faculty-directed curriculum), meet with their graduate student mentor for one-on-one academic advising, attend lectures and panel discussions featuring department faculty and alumni, and go on field trips to campus resources. Students are not required to be declared majors in order to participate.

Berkeley Connect

Schedule:

Section

Days/Times

Location

Instructor

Class

003 DIS

We 6:00PM - 6:59PM

Evans 51

Antonio Montalban, Ben Wormleighton

18956

Units

Enrollment Status

1

Open

Additional Information:

Prerequisites:

Description: Berkeley Connect is a mentoring program, offered through various academic departments, that helps students build intellectual community. Over the course of a semester, enrolled students participate in regular small-group discussions facilitated by a graduate student mentor (following a faculty-directed curriculum), meet with their graduate student mentor for one-on-one academic advising, attend lectures and panel discussions featuring department faculty and alumni, and go on field trips to campus resources. Students are not required to be declared majors in order to participate.

Berkeley Connect

Schedule:

Section

Days/Times

Location

Instructor

Class

004 DIS

Th 6:00PM - 6:59PM

Evans 41

19113

Units

Enrollment Status

1

Closed

Additional Information:

Prerequisites:

Description: Berkeley Connect is a mentoring program, offered through various academic departments, that helps students build intellectual community. Over the course of a semester, enrolled students participate in regular small-group discussions facilitated by a graduate student mentor (following a faculty-directed curriculum), meet with their graduate student mentor for one-on-one academic advising, attend lectures and panel discussions featuring department faculty and alumni, and go on field trips to campus resources. Students are not required to be declared majors in order to participate.

Introduction to Mathematical Economics

Schedule:

Section

Days/Times

Location

Instructor

Class

001 LEC

TuTh 12:30PM - 1:59PM

LeConte 251

Haluk Ergin

19090

Units

Enrollment Status

4

Open

Additional Information:

Prerequisites: Math 53 and 54

Description: Selected topics illustrating the application of mathematics to economic theory. This course is intended for upper-division students in Mathematics, Statistics, the Physical Sciences, and Engineering, and for economics majors with adequate mathematical preparation. No economic background is required.

Introduction to Abstract Algebra

Schedule:

Additional Information:

Prerequisites: 54 or a course with equivalent linear algebra content

Description: Sets and relations. The integers, congruences, and the Fundamental Theorem of Arithmetic. Groups and their factor groups. Commutative rings, ideals, and quotient fields. The theory of polynomials: Euclidean algorithm and unique factorizations. The Fundamental Theorem of Algebra. Fields and field extensions.

Introduction to Abstract Algebra

Schedule:

Additional Information:

Prerequisites: 54 or a course with equivalent linear algebra content

Description: Sets and relations. The integers, congruences, and the Fundamental Theorem of Arithmetic. Groups and their factor groups. Commutative rings, ideals, and quotient fields. The theory of polynomials: Euclidean algorithm and unique factorizations. The Fundamental Theorem of Algebra. Fields and field extensions.

Introduction to Abstract Algebra

Schedule:

Additional Information:

Prerequisites: 54 or a course with equivalent linear algebra content

Description: Sets and relations. The integers, congruences, and the Fundamental Theorem of Arithmetic. Groups and their factor groups. Commutative rings, ideals, and quotient fields. The theory of polynomials: Euclidean algorithm and unique factorizations. The Fundamental Theorem of Algebra. Fields and field extensions.

Introduction to Abstract Algebra

Schedule:

Additional Information:

Prerequisites: 54 or a course with equivalent linear algebra content

Description: Sets and relations. The integers, congruences, and the Fundamental Theorem of Arithmetic. Groups and their factor groups. Commutative rings, ideals, and quotient fields. The theory of polynomials: Euclidean algorithm and unique factorizations. The Fundamental Theorem of Algebra. Fields and field extensions.

Introduction to Abstract Algebra

Schedule:

Additional Information:

Prerequisites: 54 or a course with equivalent linear algebra content

Description: Sets and relations. The integers, congruences, and the Fundamental Theorem of Arithmetic. Groups and their factor groups. Commutative rings, ideals, and quotient fields. The theory of polynomials: Euclidean algorithm and unique factorizations. The Fundamental Theorem of Algebra. Fields and field extensions.

Introduction to Abstract Algebra

Schedule:

Additional Information:

Prerequisites: 54 or a course with equivalent linear algebra content

Description: Sets and relations. The integers, congruences, and the Fundamental Theorem of Arithmetic. Groups and their factor groups. Commutative rings, ideals, and quotient fields. The theory of polynomials: Euclidean algorithm and unique factorizations. The Fundamental Theorem of Algebra. Fields and field extensions.

Mathematical Tools for the Physical Sciences

Schedule:

Section

Days/Times

Location

Instructor

Class

001 LEC

MoWeFr 2:00PM - 2:59PM

Cory 241

Marina Iliopoulou

19036

Units

Enrollment Status

4

Open

Additional Information:

Prerequisites: 53 and 54

Description: Intended for students in the physical sciences who are not planning to take more advanced mathematics courses. Rapid review of series and partial differentiation, complex variables and analytic functions, integral transforms, calculus of variations.

Mathematical and Computational Methods in Molecular Biology

Schedule:

Additional Information:

Prerequisites: 53, 54, and 55; Statistics 20 recommended

Description: Introduction to mathematical and computational problems arising in the context of molecular biology. Theory and applications of combinatorics, probability, statistics, geometry, and topology to problems ranging from sequence determination to structure analysis.

Berkeley Connect

Schedule:

Section

Days/Times

Location

Instructor

Class

001 DIS

We 7:00PM - 7:59PM

Evans 41

18868

Units

Enrollment Status

1

Open

Additional Information:

Prerequisites:

Description: Berkeley Connect is a mentoring program, offered through various academic departments, that helps students build intellectual community. Over the course of a semester, enrolled students participate in regular small-group discussions facilitated by a graduate student mentor (following a faculty-directed curriculum), meet with their graduate student mentor for one-on-one academic advising, attend lectures and panel discussions featuring department faculty and alumni, and go on field trips to campus resources. Students are not required to be declared majors in order to participate.

Berkeley Connect

Schedule:

Section

Days/Times

Location

Instructor

Class

002 DIS

Tu 7:00PM - 7:59PM

Evans 61

18869

Units

Enrollment Status

1

Closed

Additional Information:

Prerequisites:

Description: Berkeley Connect is a mentoring program, offered through various academic departments, that helps students build intellectual community. Over the course of a semester, enrolled students participate in regular small-group discussions facilitated by a graduate student mentor (following a faculty-directed curriculum), meet with their graduate student mentor for one-on-one academic advising, attend lectures and panel discussions featuring department faculty and alumni, and go on field trips to campus resources. Students are not required to be declared majors in order to participate.

Berkeley Connect

Schedule:

Section

Days/Times

Location

Instructor

Class

003 DIS

Th 7:00PM - 7:59PM

Evans 41

18870

Units

Enrollment Status

1

Open

Additional Information:

Prerequisites:

Description: Berkeley Connect is a mentoring program, offered through various academic departments, that helps students build intellectual community. Over the course of a semester, enrolled students participate in regular small-group discussions facilitated by a graduate student mentor (following a faculty-directed curriculum), meet with their graduate student mentor for one-on-one academic advising, attend lectures and panel discussions featuring department faculty and alumni, and go on field trips to campus resources. Students are not required to be declared majors in order to participate.

Berkeley Connect

Schedule:

Section

Days/Times

Location

Instructor

Class

004 DIS

We 5:00PM - 5:59PM

Evans 55

Antonio Montalban, Ben Wormleighton

18871

Units

Enrollment Status

1

Closed

Additional Information:

Prerequisites:

Description: Berkeley Connect is a mentoring program, offered through various academic departments, that helps students build intellectual community. Over the course of a semester, enrolled students participate in regular small-group discussions facilitated by a graduate student mentor (following a faculty-directed curriculum), meet with their graduate student mentor for one-on-one academic advising, attend lectures and panel discussions featuring department faculty and alumni, and go on field trips to campus resources. Students are not required to be declared majors in order to participate.

My understanding is that through an agreement between UC and Springer, chapters of the first edition of this book are available for free download by students. They should be satisfactory - I do not plan to assign exercises from the Conway book.

Course description:

The theory of Banach algebras is a very elegant blend of algebra and topology which provides unifying principles for a number of different parts of mathematics and its applications, notably operator theory, commutative and non-commutative harmonic analysis and the theory of group representations, and the theory of functions of one and several complex variables. But at the present time probably its most extensive use is as a foundation for non-commutative measure theory (von Neumann algebras, Math 209) and non-commutative topology and geometry (C*-algebras, Math 208). These in turn provide a foundation for quantum physics, but they also have myriad applications in many other directions, including group representations and harmonic analysis, ordinary topology and geometry, and even number theory. (For a vast panorama of the applications see Alain Connes' 1994 book "Noncommutative Geometry", which is available on the web as a free download.)
I will cover the standard topics as listed in the catalog. Beyond the basic general theory of Banach algebras this will include several forms of the spectral theorem for self-adjoint operators on Hilbert space, compact and Fredholm operators, and group algebras and the Fourier transform and their relation to representation theory. Further topics as time permits, probably including Toeplitz operators and their index. The problem sets will involve a number of important specific examples beyond those presented in class.

Homework: Many weeks I will give out a problem set, and the course grade will be based on the work done on these. There will be no final examination.

Advanced Topics in Probability and Stochastic Process

Schedule:

Section

Days/Times

Location

Instructor

Class

001 LEC

TuTh 2:00PM - 3:29PM

Evans 330

Alan Hammond

18816

Units

Enrollment Status

3

Open

Additional Information:

Prerequisites: Statistics C205A-C205B.

Syllabus: The topics of this course change each semester, and multiple sections may be offered. Advanced topics in probabilty offered according to students demand and faculty availability. Also listed as Statistics C206A.

Riemannian Geometry

Schedule:

Section

Days/Times

Location

Instructor

Class

001 LEC

MoWeFr 4:00PM - 4:59PM

Evans 2

John Lott

19117

Units

Enrollment Status

4

Open

Additional Information:

Prerequisites: 214

Description: Riemannian metric and Levi-Civita connection, geodesics and completeness, curvature, first and second variations of arc length, Cartan-Hadamard theorem and the second fundamental form.
This will take up the first half of the semester. The rest of the course will be an introduction to comparison geometry.

Additional Information:

Description: Mandatory for all graduate student instructors teaching for the first time in the Mathematics Department. The course consists of practice teaching, alternatives to standard classroom methods, guided group and self-analysis of videotapes, reciprocal classroom visitations, and an individual project.